Progressive waves: phase and path difference · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading waves and their phase gaps

Science · Waves, Light & Sound · ages 16-17
Name ______________________   Date ____________

  1. A displacement record ranges from +3 cm to −3 cm about rest at zero. Its amplitude is 6 cm.

    Circle one:   True   False

  2. Stated data from a displacement-distance graph put neighbouring crests at 2 m and 8 m. What is the wavelength?

    • 6 m
    • 6 s
    • 2 cm

  3. Stated data from a displacement-time graph show neighbouring crests at 2 s and 7 s at one position. What is the period?

    • 5 m
    • 5 s
    • 7 s

  4. Two waves start in phase, share frequency and wavelength, and gain no extra phase shifts. Their paths to a meeting point differ by half a wavelength. How do they arrive?

    • In antiphase
    • In phase
    • At double amplitude

  5. Two points on one periodic progressive wave are three quarters of a wavelength apart. Apply separation ÷ wavelength × 360 directly, without reducing the result. Give the positive accumulated phase gap in degrees.

    Answer: ______________

  6. Two waves start in phase, share frequency and wavelength, and gain no extra phase shifts. Their paths differ by one wavelength. How do they arrive?

    • In antiphase
    • With zero amplitude
    • In phase

  7. Two waves start in phase, share frequency and wavelength, and gain no extra phase shifts. Their paths differ by 1.5 wavelengths. Give the residual arrival phase gap after removing whole cycles, in degrees from 0 to below 360.

    Answer: ______________

  8. Two points on one periodic progressive wave are 1.25 wavelengths apart at the same instant. After removing the whole-wavelength part, are their oscillations in phase?

    • Yes, any gap larger than a wavelength is in phase
    • Yes, discarding a full cycle discards every difference
    • No, a nonzero quarter-cycle difference remains
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading waves and their phase gaps W1-mt_RotpycCNF8-s1

  1. False · The greatest displacement magnitude from zero is 3 cm. Six centimetres is the peak-to-trough range.
  2. 6 m · Subtract neighbouring crest positions: 8 − 2 = 6 m. Distance-axis data give wavelength, not period.
  3. 5 s · The time between neighbouring crests is 7 − 2 = 5 s, which is the period.
  4. In antiphase · Under the given assumptions, a half-wavelength path difference adds half a cycle, so arrival is antiphase.
  5. 270 · The specified accumulated gap is (3/4) × 360 = 270 degrees.
  6. In phase · One wavelength adds one full cycle. Under the stated assumptions, the waves arrive in phase.
  7. 180 · Remove the whole wavelength from 1.5. The remaining half cycle gives 0.5 × 360 = 180 degrees.
  8. No, a nonzero quarter-cycle difference remains · The gap is one whole cycle plus a quarter cycle. The whole cycle changes no phase alignment, but the remaining quarter cycle prevents in-phase motion.
Worksheet · LightMySky